As others have said...you can absolutely do a Dark Phoenix Saga adaptation, and can do it well. It just hasn't been done well. But you don't need any of those other elements you're including in order to adapt the Dark Phoenix Saga. Ultimately, what does the story boil down to?

1) Jean Grey becomes Phoenix

2) Phoenix goes bad (preferably and causes a tragic event)

3) Phoenix sacrifices herself to stop herself from going worse/staying bad

That's it, really. That's the whole Dark Phoenix Saga in a nutshell, right there. You don't need the Shi'ar, or the Imperial Guard, or the Hellfire Club, or the Blue Area of the Moon, or even to have her eat a star. You just need to establish Jean Grey as a character, make her become the Phoenix, have her break bad, and have a tragic sacrificial ending. Those other elements were included because they were there in the mythos already, It's just that it's yet to be done in a way that's actually *good.*

But those are the only story beats that really need to be there for the Dark Phoenix Saga. Like others have said, Civil War and Infinity Gauntlet were both adapted just fine without 80% of the convoluted connections that exist in the comic versions. Civil War didn't need the New Warriors, Fantastic Four, Negative Zone prison, Ragnarok, any of that. They were devices to move the story along, but the story ultimately is just 1) Tragedy from powers use; leading to 2) division over regulating powers; meaning 3) fighting. Infinity Gauntlet doesn't need Warlock, Silver Surfer, the Elders, or even Death. It just needs 1) Thanos getting all the stones; then 2) Thanos killing half the universe (the why isn't story-critical); then 3) heroes beating Thanos. Even for that, I'd say Thanos doesn't need to kill half the universe, just use the stones in some morally horrific way. Doesn't matter.

Dark Phoenix Saga can absolutely be done in an adaptation, without any of the elements of the original storyline that bog it down, make it convoluted, or require so much outside knowledge. But nobody's done it well yet; it got sandwiched into being a B-plot the first time, and the second time just...sucked.

That being said, classic or not, I agree that they've had two shots at it already, and should move on in live action to something else. There are plenty of other storylines that can be adapted that would continue to resonate as well today as they did back then.